Theorems · Theorem · real analysis
ENNReal.HolderConjugate.lt_top_iff_one_lt
∀ (p q : ENNReal) [p.HolderConjugate q], p < ⊤ ↔ 1 < q
- Defined in
- Mathlib.Data.ENNReal.Holder
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 146 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- ENNReal.HolderConjugate
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites7
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- ENNRealstatement and proof · cited by 9,879
- Top.topstatement · cited by 9,680
- lt_top_iff_ne_topproof · cited by 95
- lt_iff_le_and_neproof · cited by 47
- ENNReal.HolderConjugatestatement and proof · cited by 39
- ENNReal.HolderConjugate.one_leproof · cited by 3
- ENNReal.HolderConjugate.ne_top_iff_ne_oneproof · cited by 1
Cited by2
Results whose statement or proof uses this declaration.
- ENNReal.HolderConjugate.toReal_iffproof · cited by 2
- ENNReal.HolderConjugate.toReal_of_ne_topproof · cited by 0